Quantum Information Processing最新文献

Entanglement distillation is a key task in quantum-information processing. In this paper, we distill non-positive-partial-transpose (NPT) bipartite states of some given Schmidt rank and matrix rank. We show that all bipartite states of Schmidt rank two are locally equivalent to classical-classical states, and all bipartite states of Schmidt rank three are 1-undistillable. Subsequently, we show that low-rank B-irreducible NPT states are distillable for large-rank reduced density operators by proving low-rank B-irreducible NPT state whose range contains a product vector is distillable. Eventually, we present an equivalent condition to distill (Mtimes N) bipartite states of rank (max {M,N}+1).

Characterizing quantum entanglement in mixed states is a longstanding challenge. Among the various methods available, conditional entropies serve as a powerful tool. Notably, the AR q-conditional entropy introduced by Abe and Rajagopal in 2002 has demonstrated significant promise as it often surpasses other entropy-based criteria. The wide-ranging applications of conditional entropy in quantum information underscore the importance of studying and analyzing it for a deeper understanding of quantum correlations and their implications. In this paper, we investigate the non-separability of noisy Dicke states using the AR approach of conditional entropy. Our findings reveal that the entropic criterion is equally effective as the PPT criterion in identifying non-separability across a large subset of N-partite noisy Dicke states with even N and excitation number (k = N/2). Additionally, for systems with (N > 30) and (k=1), the separability thresholds derived from both criteria converge within (10^{-8}), highlighting their strong agreement in this parameter range. Furthermore, we established a condition based on AR q-conditional entropy for identifying genuine multipartite entanglement (GME) in noisy Dicke states and compared its effectiveness to previous methods. Notably, our condition identifies a broader range of GME, particularly when the number of excitations approaches half the number of qubits (i.e., N/2). In contrast, previous methods perform better when the number of excitations is significantly less than N/2. We believe these results will pave the way for further advancements in entanglement theory and the development of potential quantum-based applications for conditional entropy.

This work introduces a dynamic hierarchical quantum secret sharing scheme that utilizes the quantum Fourier transform and the generalized Hadamard gate. In this scheme, the distributor transmits both the secrets, quantum and classical information simultaneously to the participants. The authenticity of the participants is ensured by employing the generalized Bell state. The access structure is flexible and can be modified, allowing the number of participants to increase or decrease, whenever the shared classical secret is updated, without requiring any changes to each of the individual hierarchical secrets held by participants. We examine two scenarios concerning the addition of participants: the first involves incorporating a new participant into an existing level, while the second involves introducing an entirely new level within the hierarchical structure. Additionally, the security analysis demonstrates that the proposed protocol is resilient to intercept-and-resend, collusion, entangle-and-measure, forgery, and denial attacks.

We investigate the dynamics of quantum-state texture (QST) for two uniformly accelerated atoms interacting with a quantized massive scalar field. Our analysis reveals that the system’s evolution arises from a complex competition between local decoherence caused by vacuum fluctuations and a collective, environment-mediated evolution that drives the system to a steady state. This interplay is identified as the physical origin of the notable dip-and-recover phenomenon observed in the QST for certain initial states. The results demonstrate that in the long time limit, the atoms evolve toward a thermal state at the Unruh temperature. We further show how physical parameters regulate this competition: Increasing interatomic separation and field mass can partially protect QST by weakening the collective recovery effect or universally slowing all dissipative processes, respectively. Conversely, higher acceleration enhances the collective thermalization, leading to a faster evolution toward a steady QST value. These insights are significant for understanding and controlling quantum resources in relativistic open quantum systems.

We propose a scheme that induces quantum correlations in optomechanical systems. Our benchmark system consists of two optically coupled optical cavities which interact with a common mechanical resonator. The optical cavities host saturable nonlinearity which triggers either gain or losses in each cavity. Without these nonlinearities, there are no quantum correlations, i.e., entanglement and steering, generated in the system. By turning on the nonlinearities, gain and losses are switched on, enabling flexible generation of both quantum entanglement and quantum steering in our proposal. These generated quantum correlations seem to be insensitive to the induced gain, while the induced losses through saturation effect efficiently enhance quantum correlations. Moreover, the robustness of the generated quantum correlations against thermal fluctuations is further improved under nonlinear saturation scenario. This work suggests a way of using nonlinear saturation effects to engineer quantum correlations even at room temperature, which are useful for quantum information processing, quantum computational tasks, and quantum technologies.

Uncertainty relations are pivotal in delineating the limits of simultaneous measurements for observables. In this paper, we derive four novel uncertainty and reverse uncertainty relations for the sum of variances of two incompatible observables, leveraging the mathematical framework of the Maligranda inequality. These relations are shown to provide highly precise bounds, in some cases outperforming well-known existing relations. Furthermore, we extend these results to multi-observable scenarios by employing an inequality from M. Kato et al., deriving generalized uncertainty relations that similarly exhibit enhanced precision. The incorporation of the phase angle of the measurement state contributes to strengthening the derived inequalities. Comparative analyses with prior studies confirm the effectiveness of our inequalities in two-observable systems via three illustrative examples.

In this paper, we give a polynomial time algorithm to compute (varphi (N)) for an RSA module N using as input the order modulo N of a randomly chosen integer. This provides a new insight in the very important problem of factoring an RSA module with extra information. In fact, the algorithm is extremely simple and consists only on a computation of a greatest common divisor, two multiplications and a division. The algorithm works with a probability of at least (1-frac{1}{N^{1/2-epsilon }}), where (epsilon ) is any small positive constant.

Quantum visual secret sharing is a novel and important research direction. It has higher security and practicality. However, current schemes are designed for the sharing and recovery of a single secret image. To address this problem, we propose a novel (2,2) quantum visual multi-secret sharing (QVMSS) scheme. In the sharing phase, a quantum encoding table is designed. The colors of the two secret images are entangled and encoded into four different quantum superposition states, which are then distributed to the participants. All secret images are recovered using quantum OR operation and quantum shift operation in the recovery phase. We conducted experiments on a set of 20 standard halftone images to test the feasibility of our proposed scheme. Our scheme can completely recover all the secrets while improving the efficiency and security compared to traditional schemes.

The magic state injection process is a critical component of fault-tolerant quantum computing, and numerous studies have been conducted on this topic. Many existing studies have focused on square-lattice structures, where each qubit connects directly to four other qubits via two-qubit gates. However, hardware that does not follow a lattice structure, such as IBM’s heavy-hexagon structure, is also under development. In these non-lattice structures, many quantum error correction (QEC) codes designed for lattice-based system cannot be directly applied. Adapting these codes often requires incorporating additional qubits, such as flag qubits. This alters the properties of the QEC code and introduces new variables into the magic state injection process. In this study, we implemented and compared the magic state injection process on a heavy-hexagon structure with flag qubits and a lattice structure without flag qubits. Additionally, we considered biased errors in superconducting hardware and investigated the impact of flag qubits under these conditions. Our analysis reveals that the inclusion of flag qubits introduces distinct characteristics into the magic state injection process, which are absent in systems without flag qubits. Based on these findings, we identify several critical considerations for performing magic state injection on heavy-hexagon systems incorporating flag qubits. Furthermore, we propose an optimized approach to maximize the efficacy of this process in such systems.

Quantum secret sharing plays an important role in quantum cryptography. When the deception occurs in quantum secret sharing scheme, the dishonest participant may obtain the secret exclusively. To address this, researchers have developed fair quantum secret sharing schemes to ensure the fairness of obtaining the secret among participants. However, we point that existing schemes achieve fairness at the significant cost of both efficiency and practicality. In this work, firstly, we propose a new fairness framework. Using our fairness framework, it is the first time that the scheme achieves fairness independent of the total round number k of reconstruction set in scheme. Compared to existing schemes that require big enough k to ensure fairness, our new method removes the obstacles to reducing rounds of reconstruction and significantly improving the scheme’s efficiency. Furthermore, our fairness framework can be used for all existing fair quantum secret sharing schemes to significantly reduce the rounds of reconstruction and improve the efficiency of the scheme. Secondly, we present an efficient verification mechanism for reconstructed parameters, which reduces computational cost and complexity compared to existing approaches. Lastly, combining fairness framework and efficient verification mechanism, a new and efficient fair quantum secret sharing scheme is proposed. Our scheme achieves fairness in just 2 rounds of reconstruction with less verification cost. Compared with existing fair quantum secret sharing schemes, our scheme has greatly improved the efficiency and enhanced the practicality.